Full Idea
The axiom of infinity: that there are infinite sets is to claim that completed infinite collections can be treated mathematically. In its standard contemporary form, the axioms assert the existence of the set of all finite ordinals.
Gist of Idea
Axiom of Infinity: completed infinite collections can be treated mathematically
Source
Penelope Maddy (Naturalism in Mathematics [1997], I.3)
Book Reference
Maddy,Penelope: 'Naturalism in Mathematics' [OUP 2000], p.52